What is the answer to (n+5)/(n+8)=1+6/(n+1) ?

The answer to (n+5)/(n+8)=1+6/(n+1) is n=-17/3

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(n+5)/(n+8)=1+6/(n+1)

\frac{n + 5}{n + 8} = 1 + \frac{6}{n + 1}

n = - \frac{17}{3}

Decimal

n = - 5.66666 \dots

Solution steps

\frac{n + 5}{n + 8} = 1 + \frac{6}{n + 1}

Multiply by LCM

n^{2} + 6 n + 5 = n^{2} + 15 n + 56

Move

5

to the right side

n^{2} + 6 n = n^{2} + 15 n + 51

Subtract

n^{2} + 15 n

from both sides

n^{2} + 6 n - (n^{2} + 15 n) = n^{2} + 15 n + 51 - (n^{2} + 15 n)

Simplify

- 9 n = 51

Divide both sides by

- 9

n = - \frac{17}{3}

Verify Solutions

Find undefined (singularity) points:

n = - 8, n = - 1

Combine undefined points with solutions:

n = - \frac{17}{3}

\frac{x + 3}{x - 1} = 2 x + 1

2 - \frac{8}{x} = 26

x, \frac{1}{x} = \frac{1}{y} + \frac{1}{z}

3 x^{2} - \frac{24}{x} = 0

\frac{11}{x + 4} = \frac{6}{x - 2}

What is the answer to (n+5)/(n+8)=1+6/(n+1) ?
The answer to (n+5)/(n+8)=1+6/(n+1) is n=-17/3
Solve for n: (n+5)/(n+8)=1+6/(n+1)
The solution is n=-17/3